Modes of periodic domain wall motion in ultrathin ferromagnetic layers

Magnetization reversal in a periodic magnetic field is studied on an ultrathin, ultrasoft ferromagnetic Pt/Co(0.5 nm)/Pt trilayer exhibiting weak random domain wall (DW) pinning. The DW motion is imaged by polar magneto-optic Kerr effect microscopy and monitored by superconducting quantum interference device susceptometry. In close agreement with model predictions, the complex linear ac susceptibility corroborates the dynamic DW modes segmental relaxation, creep, slide, and switching.     

Coercivity mechanisms in nanostructured permanent magnets

Coercivity mechanism in permanent magnets has been debated for many years.In this paper, various models of the coercivity mechanism are classified and re-examined by the comparison and contrast.Coherent rotation and curling models can reveal the underlying reversal mechanism clearly based on isolated grains with elliptic shapes.By contrast, the numerical methods consider inter-grain interactions while simulating the evolution of the spins and hysteresis loops with complicated shapes.However, an exact simulation of magnetic reversal in permanent nanomagnets requires many meshes to mimic the thin domain wall well.Nucleation and pinning are the two main coercivity mechanisms in permanent magnets.The former signifies the beginning of the magnetic reversal, whilst the latter completes it.Recently, it is proposed that the large difference between the intrinsic magnetic properties of the nucleation centers and those of the main phase can result in a large pinning field(self-pinning), which has the attributes of both traditional nucleation and pinning.Such a pinning explains the experimental data of permanent magnets very well, including the enhancement of the coercivity by the grain boundary pinning.     

A comparative analysis of the mechanisms of pinning of a domain wall in a nanowire

A comparative analysis of the influence of random fluctuations of the crystallographic anisotropy and surface roughnesses on the pinning of a domain wall in a nanowire has been performed in the framework of the model of a polycrystalline nanowire. The initial magnetization curve and the coercive force for these mechanisms of pinning have been calculated. A criterion has been formulated according to which surface inhomogeneities of the nanowire play the key role in the process of pinning of a domain wall. The analytical results obtained have been verified using computer simulation.     

Angular dependence of coercivity of grains in nanocrystalline permanent magnets

In this paper magnetization remanence curves were studied for nanocrystalline Pr8Fe87B5, Pr12Fe82B6 and Pr15Fe77B8. Initially the sample was at remanence following saturation along z-axis. After rotating the magnet by 5n degrees （n=0, 1, ..., 18） a field H was applied along z-axis and then decreased to zero, and the remanence Jr^n was measured as a function of H. The curves were compared with those calculated based on the nucleation of reverse domain model and domain wall pinning model. The latter model succeeds in simulation much better than the former, and it is concluded that the magnetization reversal is dominated by domain wall pinning for all the samples. The nucleation mechanism contribution, while remains small, increases with the increase of Pr content.     

Magnetic viscosity and domain wall pinning in an MnAlC permanent magnet

Magnetic viscosity in a hot extruded MnAlC permanent magnet has been measured over a temperature range from 80 to 295 K. The results are fitted to a recent theory of “strong” and “weak” domain wall pinning which allows values of the thermal activation free (“absolute zero”) coercive field to be determined from the data. If the pinning is due to strong pins, randomly distributed throughout the material, a pin density of ≈3×10¹⁵ cm^-3 is predicted. There is no obvious evidence of pin sites of this density within the grains visible in electron micrographs.If the pinning is localized (possibly at grain boundaries) then weak pinning by a similar, but localized, density of pins is predicted. Lorentz electron microscopy domain contrast in such regions might however be overwhelmed by strain contrast effects.     

Investigation of magnetization reversal process in pinned CoFeB thin film by in-situ Lorentz TEM

Exchange bias effect has been widely employed for various magnetic devices.The experimentally reported magnitude of exchange bias field is often smaller than that predicted theoretically,which is considered to be due to the partly pinned spins of ferromagnetic layer by antiferromagnetic layer.However,mapping the distribution of pinned spins is challenging.In this work,we directly image the reverse domain nucleation and domain wall movement process in the exchange biased Co Fe B/Ir Mn bilayers by Lorentz transmission electron microscopy.From the in-situ experiments,we obtain the distribution mapping of the pinning strength,showing that only 1/6 of the ferromagnetic layer at the interface is strongly pinned by the antiferromagnetic layer.Our results prove the existence of an inhomogeneous pinning effect in exchange bias systems.     

Switching current noise and relaxation of ferroelectric domains

We simulate field-induced nucleation and switching of domains in a three-dimensional model of ferroelectrics with quenched disorder and varying domain sizes. We study (1) bursts of the switching current at slow driving along the hysteresis loop (electrical Barkhausen noise) and (2) the polarization reversal when a strong electric field was applied and back-switching after the field was removed. We show how these processes are related to the underlying structure of domain walls, which in turn is controlled by the pinning at quenched local electric fields. When the depolarization fields of bound charges are properly screened we find that the fractal switching current noise may appear with two distinct universal behaviors. The critical depinning of plane domain walls determines the universality class in the case of weak random fields, whereas for large randomness the massive nucleation of domains in the bulk leads to different scaling properties. In both cases the scaling exponents decay logarithmically when the driving frequency is increased. The polarization reverses in the applied field as a power-law, while its relaxation in zero field is a stretch exponential function of time. The stretching exponent depends on the strength of pinning. The results may be applicable for uniaxial relaxor ferroelectrics, such as doped SBN:Ce. Received 7 February 2002 / Received in final form 10 April 2002 Published online 9 July 2002     

The defects influence on domain wall propagation in bistable glass-coated microwires

We studied the domain wall (DW) dynamics of magnetically bistable amorphous glass-coated Fe₇₄B₁₃Si₁₁C₂ microwires. In according to our experimental results magnetic field dependences of DW velocity of studied microwires can be divided into two groups: with uniform or uniformly accelerated DW propagation along the microwire. Strong correlation between the type of the magnetic field dependence of domain wall velocity, v(H), and the distribution of the local nucleation fields has been observed.Moreover, we observed abrupt increasing of DW velocity (jump) on the magnetic field dependences of the domain wall velocity, v(H), for the both types of the v(H) dependences. At the same time usual linear increasing of the domain wall velocity with magnetic field persists below these jumps. It was found that the jump height correlates with the location of nucleation place of the new domain wall. We have measured local nucleation field distribution in all the microwires. From local nucleation field distribution we have obtained the DW nucleation locations and estimated the jump height     

Evolution of domain walls and reversal mechanism in exchange-coupled nanolayers

The demagnetization process for an exchange-coupled double-nanolayer system with perpendicular easy axes has been investigated within a micromagnetic model. The nucleation field, coercivity and angular distribution of the magnetization, have been obtained as functions of the thickness L of the misaligned layer, the layer with the easy axis perpendicular to the applied field. It is found that the coercivity is identical to the nucleation field only for very small L. For larger L (larger than a quarter of its Bloch wall width), the nucleation field is negative while the coercivity saturates at 0.414H_K, where H_K is the anisotropy field. Thus for larger L, the coercivity mechanism is self-pinning rather than pure nucleation. This self-pinning has both attributes of traditional nucleation and pinning.     

Dynamic Phase-Mapping of Domain Nucleation in MgO：LiNbO3 Crystal by Digital Holographic Interferometry

The quantitative phase-mapping of the domain nucleation in MgO：LiNbO3 crystals is presented by using the digital holographic interferometry. An unexpected peak phase at the beginning of the domain nucleation is observed and it is lowered as the spreading of the domain nucleus. The existence of the nucleus changes the moving speed of the domain wall by pinning it for 3 s. Such in-situ quantitative analysis of the domain nucleation process is a key to optimizing domain structure fabrication.     

垂直取向Nd2Fe14B/α-Fe磁性三层膜的磁化反转

运用微磁学方法结合物质参数探究了垂直取向Nd₂Fe₁₄B/α-Fe磁性三层膜的磁化反转过程,计算出成核场、钉扎场以及磁滞回线随Ｌ^s（软磁相厚度）的变化,并与相关的实验和理论数据进行比较.由于考虑了退磁能量项,垂直取向的成核场比平行取向时低,在外磁场还没有反向时就发生了成核.随着软磁相厚度的增加,理论矫顽力从等于成核场（同时也等于钉扎场）,到等于钉扎场,再到小于钉扎场,矫顽力机理由成核变为钉扎. 关键词： 成核场 钉扎场 矫顽力 磁滞回线     

Magnetic reversal processes and critical thickness in FePt/α-Fe/FePt trilayers

Magnetic reversal processes of a FePt/α-Fe/FePt trilayer system with in-plane easy axes have been investigated within a micromagnetic approach. It is found that the magnetic reversal process consists of three steps: nucleation of a prototype of domain wall in the soft phase, the evolution as well as the motion of the domain wall from the soft to the hard phase and finally, the magnetic reversal of the hard phase. For small soft layer thickness L^s, the three steps are reduced to one single step, where the magnetizations in the two phases reverses simultaneously and the hysteresis loops are square with nucleation as the coercivity mechanism. As L^s increases, both nucleation and pinning fields decrease. In the meantime, the single-step reversal expands to a standard three-step one and the coercivity mechanism changes from nucleation to pinning. The critical thickness where the coercivity mechanism alters, could be derived analytically, which is found to be inversely proportional to the square root of the crystalline anisotropy of the hard phase. Such a scaling law might provide an easy way to test the present theory. Further increase of L^s leads to the change of the coercivity mechanism from pinning to nucleation.     

Controlled pinning and depinning of domain walls in nanowires with perpendicular magnetic anisotropy

We investigate switching and field-driven domain wall motion in nanowires with perpendicular magnetic anisotropy comprising local modifications of the material parameters. Intentional nucleation and pinning sites with various geometries inside the nanowires are realized via a local reduction of the anisotropy constant. Micromagnetic simulations and analytical calculations are employed to determine the switching fields and to characterize the pinning potentials and the depinning fields. Nucleation sites in the simulations cause a significant reduction of the switching field and are in excellent agreement with analytical calculations. Pinning potentials and depinning fields caused by the pinning sites strongly depend on their shapes and are well explained by analytical calculations.     

Dielectric response of a uniaxial ferroelectric in a magnetic field

Change in the dielectric response of a uniaxial ferroelectric in a static magnetic field has been detected. The effect has been observed in a polydomain ferroelectric crystal and is likely attributed to the action of the magnetic field on the domain wall pinning centers.     

Deroughening of domain wall pairs by dipolar repulsion

As a magnetic domain wall propagates under small fields through a random potential, it roughens as a result of weak collective pinning, known as creep. Using Kerr microscopy, we report experimental evidence of a surprising deroughening of wall pairs in the creep regime, in a 0.5 nm thick Co layer with perpendicular anisotropy. A bound state is found in cases where two rough domains nucleated far away from one another and first growing under the action of a magnetic field eventually do not merge. The two domains remain separated by a strip of unreversed magnetization, characterized by flat edges and stabilized by dipolar fields. A creep theory that includes dipolar interactions between domains successfully accounts for (i) the domain wall deroughening as the width of the strip decreases and (ii) the quasistatic and dynamic field dependence of the strip width s.     

The coercive field of sintered and melt-spun NdFeB magnets

The magnetic hysteresis loops have been investigated in the temperature range between 4.2 and 575 K for aligned sintered permanent magnets of nominal composition Nd₁₅Fe₇₇B₈ and for isotropic melt-spun ribbons of composition Nd₁₅Fe₇₆B₉. The measured temperature and field dependence of the coercive field is analysed within the framework of theoretical results for nucleation fields of the ideal Nd₂Fe₁₄B matrix and, of disturbed surface regions of Nd₂Fe₁₄B grains. Furthermore the pinning of domain walls at thin soft magnetic grain boundary phases is considered for the high temperature range. It is concluded that for both types of NdFeB magnets the relevant magnetic hardening mechanisms at lower temperatures are nucleation processes in magnetically inhomogeneous regions whereas at higher temperatures the pinning of domain walls at grain boundaries predominates. The critical temperature where the change of nucleation hardening to pinning hardening occurs depends sensitivity on the crystal anisotropy, the grain boundary microstructure and the macroscopic grain- and multi phase arrangements.     

Chiral domains in cycloidal multiferroic thin films: switching and memory effects

Cycloidal magnetic order occurring in some AMnO(3) perovskites is known to induce ferroelectricity. The polarization is perpendicular to the propagation vector direction of the cycloid and its chirality, and therefore it is directly related to the chiral domain structure. We show that the switching process of chiral domains is sensitively dependent on the magnetoelectric history of the sample. Moreover, by appropriate field cycling, magnetic order can display partial chiral memory. We argue that memory results from electric field coupling of cycloidal domain and nucleation and pinning of chiral domain walls, much like the domain structure in other ferroic systems.     

Modeling of irreversible switching and viscosity phenomena in perpendicular thin films

We have developed a simple numerical model for simulating domains as well as remanence and viscosity curves in the slow dynamics regime, for thin films characterized by perpendicular magnetization and irregular domain configurations due to strong disorder. The physical system is represented as constituted of identical switching units, described by proper switching field distributions and energy barrier laws for pinning and nucleation processes. The model also includes an effective field which accounts for magnetic forces proportional to magnetization, on average. Simulations of DCD curves show that when the reversal of magnetization is governed by pinning, the coercive field depends on the physical size of the film area on which the external field is applied. In the case of viscosity phenomena described by a linear energy barrier law associated with a single predominant reversal process (pinning or nucleation), universal viscosity curves can be generated by properly transforming the DCD curve of the system. We also demonstrate that a reduction of the maximum viscosity coefficient can coexist with a reduction of the energy barrier heights.     

Domain wall resistance in perpendicular (Ga,Mn)As: Dependence on pinning

We have investigated the domain wall resistance for two types of domain walls in a (Ga,Mn)As Hall bar with perpendicular magnetization. A sizeable positive intrinsic DWR is inferred for domain walls that are pinned at an etching step, which is quite consistent with earlier observations. However, much lower intrinsic domain wall resistance is obtained when domain walls are formed by pinning lines in unetched material. This indicates that the spin transport across a domain wall is strongly influenced by the nature of the pinning.     

Magnetic field dependence of the domain wall resistance in a quantum wire

For an ideal one-dimensional ferromagnetic wire with a magnetic domain wall (DW), contribution of the DW to the resistivity of the system has been investigated. We have studied the resistance due to the magnetic impurities in the domain wall which was suspended in a weak magnetic field for two types of chiralities. The analysis has been based on Boltzmann transport equation, within the relaxation time approximation. Through this formalism, both increasing and decreasing of the resistance due to the DW have been predicted in presence of Zeeman interaction as an extrinsic mechanism.